Selfdual Einstein metrics with torus symmetry
| dc.creator | Calderbank, David M. J. | |
| dc.creator | Pedersen, Henrik | |
| dc.date | 2001-05-31 | |
| dc.date.accessioned | 2026-07-07T06:23:55Z | |
| dc.date.available | 2026-07-07T06:23:55Z | |
| dc.description | It is well known that any 4-dimensional hyperkahler metric with two commuting Killing fields may be obtained explicitly, via the Gibbons-Hawking Ansatz, from a harmonic function invariant under a Killing field on R^3. In this paper, we find all selfdual Einstein metrics of nonzero scalar curvature with two commuting Killing fields. They are given explicitly in terms of a local eigenfunction of the Laplacian on the hyperbolic plane. We discuss the relation of this construction to a class of selfdual spaces found by Joyce, and some Einstein-Weyl spaces found by Ward, and then show that certain `multipole' hyperbolic eigenfunctions yield explicit formulae for the quaternion-kahler quotients of HP(m-1) by an (m-2)-torus first studied by Galicki and Lawson. As a consequence we are able to place the well-known cohomogeneity one metrics, the quaternion-kahler quotients of HP(2) (and noncompact analogues), and the more recently studied selfdual Einstein hermitian metrics in a unified framework, and give new complete examples. | |
| dc.description | 23 pages, 3 figures, AMS-LaTeX and diagrams.sty | |
| dc.identifier | https://arxiv.org/abs/math/0105263 | |
| dc.identifier | http://arxiv.org/abs/math/0105263 | |
| dc.identifier | J. Diff. Geom. 60 (2002) 485-521. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/96376 | |
| dc.subject | Differential Geometry | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | Mathematical Physics | |
| dc.subject | 53C25; 53C26, 53A30 | |
| dc.title | Selfdual Einstein metrics with torus symmetry | |
| dc.type | text |